{"title":"Sakai’s theorem for $\\mathbb{Q}$-divisors on surfaces and applications","authors":"Fei Ye, Tongde Zhang, Zhixian Zhu","doi":"10.4310/AJM.2018.V22.N4.A8","DOIUrl":null,"url":null,"abstract":"In this paper, we present a characterization of a big Q-divisor D on a smooth \nprojective surface S with D2 > 0 and H1(OS(−D)) = 0, which generalizes a result of Sakai \n[Sak90] for D integral. As applications of this result for Q-divisors, we prove results on base-pointfreeness and very-ampleness of the adjoint linear system |KS + D|. These results can be viewed as \nrefinements of previous results on smooth surfaces of Ein-Lazarsfeld [EL93] and Ma¸sek [Ma¸s99].","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2018-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asian Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/AJM.2018.V22.N4.A8","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper, we present a characterization of a big Q-divisor D on a smooth
projective surface S with D2 > 0 and H1(OS(−D)) = 0, which generalizes a result of Sakai
[Sak90] for D integral. As applications of this result for Q-divisors, we prove results on base-pointfreeness and very-ampleness of the adjoint linear system |KS + D|. These results can be viewed as
refinements of previous results on smooth surfaces of Ein-Lazarsfeld [EL93] and Ma¸sek [Ma¸s99].
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